There is no actual evidence, but logic says
Lysandre did die in the blast fired by the Ultimate Weapon, and can be proven through logic.
Reason One: The Force of the Impact
The pure power of the Infinity Energy (as it is identified in ORAS) is so incredibly powerful as to being able to wipe out the planet. Lysandre took a direct hit.
Reason Two: The Whopping Crater
As can be plainly seen, only a huge hole in the ground signifies the last known wherebouts of Lysandre. That's a pretty big clue.
Reason Three: Lysandre was still in the Ultimate Weapon when it exploded.
Lysandre didn't escape with you and your friends, he was still inside screaming and throwing a tantrum. It is also said that there is only one entrance to the hiding place of the Ultimate Weapon.
In summary, all the clues point to Lysandre's demise, therefore the most logical conclusion is that he died in the blast. However, there is no confirmation anywhere that he did, in fact, perish. It is merely (heavily) implied.
But we still don't know what that wierd mech suit of his does…